Solving Equations

The basic rule of solving equations is that you can do (almost) anything you like to both sides of an equality without changing the equivalence of the two sides. In order to isolate a particular variable, you simply identify what operations are done to that variable and then perform the inverse operations on both sides of the equation. So if you want to isolate \( x + 3 \), simply subtract 3 from both sides of the equation.

Here is a basic one-variable example:

What value of \(x\) satisfies \(3x+7=46\)?

Solving for \(x\), we have: \[\begin{align}
3x + 7 &= 46\\
3x &= 46-7\\
3x &= 39\\
x &= 13\quad_\square\
\end{align}\]

Note by Arron Kau
3 years, 10 months ago

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